On the Determination of External Forces - Application to the Calibration of an Electromagnetic Actuator

A method for obtaining an accurate estimate of forces acting upon a vibrating structure is derived in this paper. The method was developed as a means for calibrating an electromagnetic excitation device where the electromagnetic force was sought to be estimated. The unique features of the proposed method are: (a) Compensation of inertial effects; (b) Based on indirect measurement of forces and displacements in conjunction with an accurate dynamical model. The precise account of inertia and elastic effects allows us to model the relationship between the actuall applied forces and various parameters affecting the external forces. In the case of an electromagnetic device those will be ai -gap, current and magnetic flux. The lack of information in this case had lead us to a threefold approach where experimental data is combined with an analytical approach togethe with state-of-the-art measurement-equipment techniques. The necessity to obtain an accurate account of the distribution of inertia in the structure necessitates a precise spatial model extracted by means of a scanning lase - Doppler sensor. The analytical part involves the estimation of Lagrange multipliers with the extended principal of virtual work.